# Asymptotic behavior for a modified Maki-Thompson model with directed inter-group interactions

## TL;DR

This paper introduces a modified Maki-Thompson rumor model with directed inter-group contacts, analyzing how the presence of two differentiated groups affects rumor spread and the final proportion of ignorants.

## Contribution

The work extends the classic Maki-Thompson model by incorporating directed inter-group interactions and analyzes the impact on rumor dissemination.

## Key findings

- Quantifies the final proportion of ignorants in both groups.
- Demonstrates the influence of directed contacts on rumor spread.
- Provides examples and potential applications of the model.

## Abstract

In this work we propose a new extension for the Maki-Thompson rumor model which incorporates inter-group directed contacts. The model is defined on an homogeneously mixing population where the existence of two differentiated groups of individuals is assumed. While individuals of one group have an active role in the spreading process, individuals of the other group only contribute in stifling the rumor provided they would contacted. For this model we measure the impact of dissemination by studying the remaining proportion of ignorants of both groups at the end of the process. In addition we discuss some examples and possible applications.